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Freely acting automorphisms of abelian C*-algebras

Published online by Cambridge University Press:  22 January 2016

Masatoshi Enomoto  and
Kazuhiro Tamaki
Masatoshi Enomoto
Affiliation:
Department of Mathematics, Osaka Kyoiku University
Kazuhiro Tamaki
Affiliation:
Department of Mathematics, Osaka Kyoiku University
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Very recently, M. Choda, I. Kasahara and R. Nakamoto [3] extend the concept of free action of automorphisms for C*-algebras and prove several theorems which are hither to known for von Neumann algebras. In the present note, we shall concern with freely acting automorphisms on abelian C*-algebras. In § 2, several equivalent conditions for the free action are obtained. In §3, we shall apply them to an automorphism which has a transversal group.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 7 - 11
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Arveson, W. B., A theorem on the action of abelian unitary groups, Pacific J. Math., 16 (1966), 205–212.Google Scholar
[2] Choda, H., On freely acting automorphisms of operator algebras, to appear.Google Scholar
[3] Choda, M., Kasahara, I. and Nakamoto, R., Dependent element of an automorphism of a C*-algebra, Proc. Japan Acad., 48 (1972), 561–565.CrossRefGoogle Scholar
[4] Kallmann, R., A generalization of free action, Duke Math. J., 36 (1969), 781–789.Google Scholar
[5] Kowada, M., Spectral type of one-parameter group of unitary operators with transversal group, Nagoya Math. J., 32 (1968), 141–153.CrossRefGoogle Scholar